## Two S-wave eigenvectors of the Christoffel matrix
need not exist in anisotropic viscoelastic media

**Ludek Klimes**
### Summary

The 3×3×3×3 frequency-domain stiffness tensor
is complex-valued in viscoelastic media.
The 3×3 Christoffel matrix is then also complex-valued.
Using a simple example,
we demonstrate that a complex-valued Christoffel matrix need not
have all three eigenvectors at an S-wave singularity,
and we thus cannot apply the eigenvectors to calculating
the phase-space derivatives of the Hamiltonian function.

### Keywords

Attenuation, anisotropy, wave propagation, ray theory, ray tracing.

### Whole paper

The reprint is available in
PDF (88 kB).

*Stud. geophys. geod.*, **65** (2021), 291-295.